effects do hold a real relation to each other. We spoke of LAH passing (by change of movement) from the "abandonment" of sorrow to the "abandonment" of joy. We have now seen the mental effect of DOH, ME, and sон passing from the "dig. nified and solemn" to the "bold and decisive," and, by using a yet quicker movement still, we may find these same notesnever, mark you, passing into that emotional character which belongs to TE, RAY, FAH, and LAH, but-expressing that bold hearty laughter "holding both its sides," of which Milton wrote and Handel sung.

As springs the flame above a burning pile, And shoutest to the nations, who return

Thy shoutings, while the pale oppressor | flies.

Thy birthright | was not given by human hands: Thou wert twin-born with man. In pleasant fields, While yet our race was few, thou sat'st with him, To tend the quiet flock | and watch the stars, And teach the reed to utter simple airs. Thou by his side, amid the tangled wood, Didst war upon the panther and the wolf, His only foes; and thou with him didst draw The earliest furrows on the mountain side, Soft with the deluge. Tyranny himself, Thy enemy, although of reverend look, Hoary with many years, and far obeyed, Is later born than thou; and as he meets The grave defiance of thine elder eye, The usurper trembles in his fastnesses. Oh! not yet | May'st thou unbrace thy corslet, nor lay by Thy sword; nor yet, O Freedom! close thy lids In slumber; for thine enemy | never sleeps, And thou must watch and combat || till the day Of the new earth and heaven. But wouldst thou rest Awhile from tumult and the frauds of men, These old and friendly solitudes | invite

1

The laughter having thus commenced with the last phrase, which is repeated in the other "parts" also, next changes to another key (that of the sub-dominant), but still keeping DOH, SOH, ME, as its accented notes. It afterwards falls into laughter of a different style, which is more musical, perhaps, but not so open and hearty. Enough of the example is given to show the character of DOH, ME, and Soн in rapid movements.

We trust that our pupils will study all these examples with great care, and practise them well. They could not have better exercises for voice or ear. An earnest endeavour to study the mental effect of notes will very greatly increase the power of singing those notes with accuracy.

1. The most perfect consonance (or sounding together) of any two notes, is that of two which are octaves to one another-as DOH and Dон', Sон and soн1, etc. The notes agree so “per. fectly" as to be constantly regarded as the same. The consonance which stands next in the order of agreement is that of the fifth-DOH with SOH, RAY with LAH, ME with TE, SOH with RAY1, and LAH with ME'. TE with FAH1 is an imperfect fifth. Approaching to this in "perfectness" of concord, is the fourthDOH with FAH, RAY with SOH, ME with LAH, SOH with DOH', LAH with RAY', and TE with ME. FAH, TE, is an augmented fourth. But it is not the most "perfect" consonance that is the most pleasing. For the production of pleasure and beauty in music, as in all other fine arts, there is needed a certain variety in unity-a certain difference blending with agreement. Hence it is that the most pleasing consonance of the scale is that of the third-DOH with ME, RAY with FAH, ME with SOH, etc. The first, third, and fifth of the scale-DOH, ME, SOн-form, when sounded together, the most delightful union of sounds that is known. A consonance of three or more notes is called a "chord."

2. Try each of the above consonances in order, either by the help of a friend or with some musical instrument. You will thus be aided in forming a kind of personal acquaintance with the notes. You will be enabled to individualise them, and to recognise by the ear their mental effect.

3. The ancient and well-known tune, "Prospect," is introduced to illustrate still further the qualities of DOH, ME, and

The first song is taken from the "Hymns for Infant Minds," by Jane Taylor and her sister, Mrs. Gilbert, a work, like all by the same authors, of priceless value in aid of education in school or family. But for the sake of those who would sing this tune to a sacred hymn, we add the exquisite words composed for this tune by the late Thomas Rawson Taylor, of Bradford, Yorkshire-hitherto treasured, like his other poems, by a select circle, but henceforth, we trust, more widely to be known. This tune must be thoroughly sol-faed by heart," like the rest, and the pupil must point to the notes on the modulator as he thus sol-faes.

Our pupils must expect no explanation, at this stage of the course, of the sharps, or flats, or clefs, introduced at the beginning of the old notation staff. A proper explanation now would be lengthy and out of place. They are introduced thus early for the sake of those who play on instruments. It is enough for the singer that the square mark shows him the place of the key-note.

LESSONS IN LATIN.-XIX.

THE LATIN VERB.

IN form, the Latin verb has two chief divisions-1, active; 2, passive. Thus, laudo is I praise, in the active voice, and laudor, I am praised, in the passive voice. There are some verbs which, though passive in form, are active in signification; as hortor, I encourage. The ending in r shows that hortor is of the passive form. This form the verb, so to say, lays down, or lays aside, and hence it is called deponent (from de, down, and pono, I put). Deponent verbs, then, are verbs which, disregarding the claims of their form, have an active import, just as if they were active in form. As these verbs have an active meaning, their past participle has an active meaning: thus, hortatus, the past participle of hortor, is not being encouraged, but having encouraged. This past participle joins with parts of the verb sum, I am, to form the perfect tense: thus, hortatus sum means I have encouraged. There are deponent verbs in all four conjugations.

The tenses of the verb in Latin are pretty much the same as in other languages. Thus we have PRESENT, amo, I love, or I am loving; IMPERFECT, amabam, I was loving, or I did love; PERFECT, amavi, I loved, or I have loved; PLUPERFECT, amaveram, I had loved; FIRST FUTURE, amabo, I shall or will love; SECOND FUTURE, amavero, I shall have loved.

The present tense denotes either an action continued in the present time, or an habitual action. The imperfect tense denotes an action continued in past time. The perfect tense has two meanings first, it signifies an action done and completed in past time indefinitely, and from the period in past time being indefinite or undefined, it is called an aorist, or is said to have an aorist import (aorist is a Greek word, denotes a tense of the Greek verb, and signifies undefined or indeterminate); in the second place, the perfect tense indicates an action which in itself, or in its consequences, continues from the past to the present, being somewhat the same as our phrase, I have dined— that is, I have just dined; in contradistinction to the aorist I dined that is, yesterday, or some time in the past.

The Latin has three moods, the indicative, or the mood of reality, the mood of simple statement; the subjunctive, or mood of dependence; and tho imperative, or mood of command. Mood is a Latin word (modus), signifying measure or manner. It is found in the French term mode, sometimes used in English. The term mood, therefore, denotes the modes or manners in which a statement is made. All propositions may be reduced to two general classes; they are either independent or dependent. The independent are in the indicative mood; that is, the mood which simply indicates or points out. The dependent are in the subjunctive. The word subjunctive (Latin, sub, under or to, and jungo, I join) signifies that which is subjoined; that which is connected in the way of dependence. The subjunctive mood, consequently, is the mood which is dependent on the indicative. The imperative mood, though differing in form from the other two, may logically be considered as a subdivision under the subjunctive. How closely the subjunctive and the imperative are allied, may be seen in the fact that the subjunctive is often used for the imperative; it is so used when a kind of softened command is desired. In the older Latin grammars, you will find

the potential mood, and even the optative mood; but these are mere figments; they have no corresponding reality in the language. Another form of the verb has a better claim to be termed a mood; I allude to what is called the infinitive, as legere, to read. This, however, might probably be more rightly described as the verb in its abstract form. If, however, it is acknowledged to be a mood, then we must say that the Latins have four moods, the indicative, the subjunctive, the imperative, and the infinitive. The infinitive, however, must stand in the class of dependent modes of utterance, since it makes no sense unless when joined to a verb in another mood. Thus, vult legere, he wishes to read. Here legere has meaning by being united with vult. Vult is said to be a finite word, as legere is said to be an infinitive; finite and infinitive are the opposites of each other. The two words come from the same Latin word finis, end or limit; the former, therefore, means the limited; the latter, having the prefix, in, not, means the unlimited; that is, the definite and the indefinite mood.

Another form in which the verb appears is the participle. In Latin there are four participles; 1, the active, ending in ns, as amans, loving; 2, the passive, ending in tus, as amatus, loved; 3, the future, ending in rus, as amaturus, about to love; and 4, the corresponding passive participle, which ends in dus, as amandus, to be loved-that is, he who ought to be loved. The usages connected with these participles will be set forth hereafter. The Latins have no active participle of past time; they cannot by means of a participle say having loved. But the past participles of their deponent verbs have an active signifi cation, since the verbs themselves have an active signification; thus, hortatus means having exhorted.

Connected in form with the passive participle in dus, is what in Latin is called the gerund; as, amandum, which wears the appearance of being the neuter singular of the participle amandus. The gerund exists in the nominative as amandum, in the genitive as amandi, and in the dative and ablative as amando. It is not easy to set forth the distinctive meaning of the gerund in one English term. Its proper and full force must be learnt in reading Latin prose. I place before you a few instances of its use.

GERUND.

Scribendum est, one must write.
Scribendi ars, the art of writing.

Scribendo aptus est, he is ready at writing.
Inter scribendum, during writing.

Scribendo exerceor, I am exercised in writing.

Hence, you see that the gerund denotes under certain circum stances the whole act implied in the verb, as here the act of writing. Yet is it nearly connected in meaning as in form with participles. Similar, indeed, is the case with our word writing; and generally our active participles in ing, besides having a participial force, assume now a verbal, and now a substantive force; a verbal, as in writing the letter, say, etc.—that is, while you write, or when you write; a substantive force, as, the writing is bad.

As in form the gerund, so also the supine is peculiar to the Latin tongue. There are two supines, one ending in um, as amatum, in order to love; the other ending in u, as amatu, te love or to be loved; the former is called the first or active supike; the latter, the second or passive supine. The former is used after verbs of motion; the latter is used after certain adjectives; thus:

SUPINES.

1st. Venio rogatum, I come in order to ask.

2nd. Jucunda auditu, pleasant to hear or to be heard. You may see here an illustration of the propriety of my ques tioning whether the infinitive should be designated a mood. If it is a mood, is not the supine equally a mood? And if you admit the claims of the supine, can you deny the claims of the gerund? But if the gerund is a mood, equally is the participle a mood. Properly there can be no mode or manner of utterance where there is not a complete utterance; that is to say, moods imply propositions, for without a proposition there is no mood. If so, the infinitive can be called a mood only by some latitude of expression.

These, then, are the forms of the verb which you have to understand, to recognise, to construe, to form, and to employ in Latin. I will here recapitulate them :

1. The Indicativo. 2. The Subjunctive. 3. The Imperative.
FOUR OTHER FORMS.

1. The Infinitive. 2. The Participle. 3. The Gerund. 4. The Supine. In all, fifteen varieties of expression enter into the Latin verb. You are not to suppose from this that every verb has all these forms. Even when the Latin was a living language, many verbs were defective, that is, lacked some of the ordinary forms. We, however, are bound to write the language as we find it written in the remains of Roman literature, and so are restricted to forms which actually occur in extant Latin writings; and as poetry has its licences, so are we obliged, in order to be correct, to confine ourselves to the usages of the best prose writers. In general, the Latin of Cicero is the model to be

followed.

Verbs which have been above described as active, may also be called transitive; that is, active in voice, and transitive in import; thus, laudo puerum, I praise the boy, is a transitive verb, because the action of the verb passes over (trans, across, over, and eo, I go) to the object, puerum. As some verbs are transitive, others are intransitive or not transitive. Such is dormio, I sleep, in which no action passes over to an object. Intransitives are sometimes called neuters; that is, neither active nor passive. When they have a passive form, they bear the name of neuter passives; as, ausus sum, I have ventured; gavisus sum, I have rejoiced. Sometimes a verb, in the passive form, has a reflective force, and may be Englished by a neuter or intransitive verb; as, moveor, I move myself, or simply, I A few active forms have a passive signification; as, vapulo, I am beaten; veneo, I am sold. Somewhat similar is fio (factus sum, fieri), I become, I pass from one state into another; I am made.

move.

KEY TO EXERCISES IN LESSONS IN LATIN.-XVIII. EXERCISE 69.-LATIN-ENGLISH.

1. There is no firm friendship among the bad. 2. I hasten to death. 3. The Gauls dwell beyond the Rhine. 4. We have no weapons against death. 5. A generous man is mild toward the conquered. 6. Comets are admirable on account of their rarity and beauty. 7. Slaves obey on account of fear, the good from a regard to duty. 8. Sailing along the shore is often dangerous. 9. No one is happy before death. 10. On what account dost thou laugh? 11. Below the moon all things 13. are perishable. 12. Thou dwellest many years among barbarians. The kingdom of Pluto is placed under the earth. 14. The government of nations is in the power of kings. 15. Fish die out of water. 16. hatred to horses. The thing happened contrary to expectation. 17. The camel bears 18. Painted garments are mentioned with (in) Homer. 19. Many animals congregate and fight against other animals. 20. The hippopotamus feeds on the corn-fields around the Nile. EXERCISE 70.-ENGLISH-LATIN.

1. Inter malos nulla est firma societas. 2. Contra mortem nulla habet homo arma. 3. Ultra mortem est vita. 4. Ad Rhenum properamus. 5. Ante domum sunt amici. 6. Apud me sunt filii mei. 7. Apud te suntne filii vestri? 8. Mitis erga victos est rex. 9. Post mortem boni sunt felices. 10. Quid est infra terram ? 11. Deus est Penes me mei sunt liberi. super omnia et per omnia. 12. Infra nubes habitant homines. dicta. 15. Rus propter te amo. 14. Apud Ciceronem sunt multa pulchra 16. Intra muros sunt milites. EXERCISE 71.-LATIN-ENGLISH.

13.

1. Poison is for (acts as) a remedy sometimes. 2. An infant has no 4. power without another's aid. 3. Eagles do not build in trees. The cuckoo lays in the nests of other birds. 5. By old age our senses grow dull. 6. Some men are born with teeth. 7. Xerxes fled from Greece with very few soldiers. 8. Metellus leads elephants in triumph. 9. The traveller sings in presence of the robber. 10. The stars move from the east (rising of the sun) to the west (setting of the sun). 11. Britain was discovered by the Phoenicians. 12. Bees cannot exist 13. It is sweet to die for one's country. without a queen. EXERCISE 72.-ENGLISH-LATIN.

6. Ab ortu

1. Estne aliquando venenum pro remedio ? 2. In Græcia pugnat Xerxes. 3. In senectute visus et auditus hebescunt. 4. Paritne in alieno nido coccyx? 5. Soror tua coram multis cantat. solis ad occasum properant. 7. Græcia proficiscens exercitus in Italiam 8. Metellus cum multis militibus est in Britannia. properat. 9. Filius meus sine dentibus est natus. 10. Estne exercitus sine elephantis? 11. Elephanti in triumpho a duce ducuntur. 12. Dulcene est pro patria mori? 13. Quid sine Dei ope sunt mortales? 14. Omnesne aves in arboribus nidificant? 15. Clam patre est puer in domo. 16. Infantes in gremio matris felices est dulce videre. 17. Tecumne est soror tua? 18. Sine patre nihil potest puer. 19. Mecum est filia mea. 20. Quot liberi tecum sunt? 21. Quot homines sunt in Britannia ?

LESSONS IN GEOMETRY.-XIX.

Now similar tenses should follow each other, and not dissimilar ones. That is, if you use one present, use another; if you use a present, do not let an imperfect immediately follow. Observe, however, that the present infinitive may come after a finite verb in the imperfect tense, as solebat scribere, he was wont to write. The rule I have now given relates to what is called the consecutio temporum, or sequence of tenses. Compare Exercise 75 (Latin-English), in the next lesson.

involves the use of the circumscribing circle, on the circumference of which the angular points of the pentagon may be marked. We have added this to the modes of construction given in the last lesson to show the student that there are many ways of constructing each of the regular polygons, and to urge him to exercise his ingenuity in finding out other methods for the construction of the hexagon, heptagon, etc., than those we are about to give him in this and the following lessons.

N

KLY intersect in the point q. From the centre Q, with the distance Q A, or Q B, describe the circle A N B, and along its circumference set off the arcs A M, M N, N o, each equal to A B, to determine the angular points M, N, O of the pentagon A M N O B, which is completed by joining the straight lines A M, M N, NO, O B. The student who is acquainted with the method of drawing the equilateral triangle, square, and regular pentagon, will readily see that the construction of figures, the number of whose sides are multiples of 3, 4, and 5, depends merely on the repeated bisection of arcs of circles or angles, as may be seen by M an inspection of Figs. 69, 70, and 66. In Fig. 69, ABC is an equilateral triangle, or trigon, inscribed in the circle AB C. By bisecting the arcs A B, BC, CA, in the points D, E, F, and joining A D, D B, BE, E C, C F, and F A, Fig. 69. we get the hexagon ADBE CF, the number of whose sides is 3 x 2, or 6. If the arcs A D, D B, B E, E C, C F, and F A, were again bisected in the points G, H, K, L, M, N, we should get a dodecagon, or twelve-sided figure, the number of whose sides is 3 x 2 x 2 =12; by joining the extremities of the arcs A G, G D, etc., or drawing chords subtending these arcs, and by another bisection of the twelve arcs, into which the circle is divided by the angular points of the dodecagon, we should get a twenty-four-sided figure. The same results would be obtained by bisecting in succession the angles at the point o, the centre of the circle, and drawing chords, as before, to the arcs obtained by the successive bisections of the angles at the centre, and the consequent bisections of the arcs on which they stand.

If the arcs AB, BC, C A, or the angles A O B, BO C, COA, were trisected, instead of being divided into two equal parts, and chords were drawn subtending the arcs thus subdivided, we should have a nonagon or enneagon, a polygon the number of whose sides is equal to 3 x 3, or 9, and by bisecting the nonagon we should obtain an eighteen-sided figure, the number of whose sides is equal to 3 x 3 x 2, or 18.

E

Similarly in Fig. 70, in which the square A B C D is inscribed in the circle A B C D, an octagon, A E B F C G D H, is obtained by bisecting the arcs A B, BC, CD, DA, in the points E, F, G, H, and joining the straight lines A E, E B, etc., the octagon being a figure the number of whose sides is 4 x 2, or 8. A further bisection of the arcs AE, E B, etc., would give us a B figure the number of whose sides is 4× 2 × 2, or 16; and so on.

Fig. 70.

D

In the same way, an inspection of Fig. 66, in Problem XLVII., page 149, shows that if we bisect the arcs A B, BC, CD, DE, EF, in the points R, S, T, P, Q, and join their extremities, we get a decagon, or regular polygon, the number of whose sides is 5 x 2, or 10; while if the arcs A B, BC, etc., were trisected, we should obtain a quindecagon, or regular polygon, the number of whose sides is 5 x 3, or 15. The learner can readily calculate for himself the results of further subdivisions of the arcs of the circle in the cases of the pentagon, decagon, and quindecagon.

The reader may have noticed already, that of all figures having equal sides and equal angles there are only three kinds that can be fitted together so as to cover a flat surface without any interstices or openings between the pieces used. These are the equilateral triangle, the square, and the hexagon. This number of regular figures that will cover a flat surface without the addition of any other figures, regular or irregular, may be further reduced to two when we remember that the hexagon itself is composed of six equilateral triangles, as may be seen from Fig. 71, in which the thick lines show how any number of equilateral triangles regularly disposed in rows may be grouped into hexagons. The learner will find it a useful practice to make drawings of the various regular polygons arranged in

Fig. 71.

order, in such patterns as his taste and fancy may dictate, for models of tesselated pavement, marquetry, and parquetry. An illustration of our meaning will be found in Fig. 72, a design which consists of perpendicular lines of pentagons, black and white in alternation, the lozenges or rhombuses (see Definition 30, Vol. I., page 53) being divided by transverse perpendicular and horizontal lines into right-angled triangles, which are also black and white in alternation as they are contiguous to a white or black pentagon respectively. The designs made by the learner, for pavement, may be done in pieces of red, black, and white paper, or in paper coloured to imitate various kinds of marble, pasted together on cardboard. The patterns for marquetry, which consists of various kinds of ornamental wood cut in small pieces and veneered on a flat surface of deal or some common timber, to form the top of a table or the panel of a cabinet; and those for parquetry, or blocks of wood about an inch in thickness, put together in symmetrical patterns to form floors, may be cut out in paper stained in imitation of various kinds of wood. It may be said that coloured paper in imitation of wood may be purchased of any one who sells materials for bookbind. jag, while paper in imitation of marble may be procured at the same place for fine work, and from the paper-hanger for making designs on a large scale. We have called the attention of the reader to the method named above of making geometrical designs in coloured paper, to show him how readily a knowledge of geometry may be applied to art purposes.

Fig. 72.

For filling up any space with small compartments all of the same size and form, the hexagon is the most convenient, because its shape assimilates more closely than either the equilateral triangle or the square to that of the circle, the strongest form for the arrangement of material to bear pressure, as in the case of the barrel drain or circular sewer. Less material, too, would be used in forming a number of hexagonal compartments than in filling the same space with compartments in the form of equi lateral triangles or squares having the same depth and area of base as the hexagon. A remarkable instance in nature of the use of the hexagon for making the most of space for stowage, with the least possible quantity of material, is found in the honey. comb, of which the cells are hexagonal in form, terminating at the bottom in a roof or floor, consisting of three parallelograms, the opposite angles of which are about 110° and 70° respectively.

The construction of a hexagon is easy enough, whether it be required to inscribe it in a given circle, or to construct it on a given straight line, because the radius of the circumscribing circle is always equal to the side of the hexagon that it sur rounds. Thus, if we have to inscribe a hexagon in the circle ACE (Fig. 73), it is manifest that all we have to do is to open the compasses to the extent of A G, the radius of the circle A CE, and divide the circumference into six equal parts by apply. ing the opening of the compasses round the circumference, and marking the points A, B, C, D, E, F, in succession. The hexagon is then completed by joining A B, B C, C D, DE, E F, FA, the chords of the six equal parts into which the circumference has been divided.

Fig. 73.

PROBLEM LI.-To construct a hexagon on a given straight line. Let A B (Fig. 73) be the given straight line on which it is required to construct a hexagon. From A and B as centres, with the distances A B and B A respectively, draw two arcs intersecting each other in G. The point G is the centre of a circle circumscribing the required hexagon. From the centre G with the distance G A describe the circle A CE; then from A and B as centres, with the radius A B and B A respectively, draw arcs cutting the circumference of the circle ACE in the points F and c; and from these points as centres, with the same radius, draw arcs cutting the circumference in the points x and D. Join AB, BC, CD, DE, E F, FA; ABCDEF is the hexagon required, for it is constructed on the given straight line A B.